The values of f(x) at the nodal points are
x: 0 0.25 0.5 0.75 1
f(x): 1 0.8 0.67 0.57 0.5
The approximate area bounded by the curve,the X-axis and the lines $x = 0$ , $x = 1$ using Simpsons rule is

0.693 sq. units

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0.793 sq. units

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0.0693 sq. units

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0.593 sq. units

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Solution

The correct option is A 0.693 sq. units
Area $= \frac{h}{3} [S + 2 S_{o} + 4 S_{e}]$
$= \frac{0.25}{3} [1.5 + 2 (0.67) + 4 (1.37)]$
$= \frac{25}{300} [1.5 + 1.34 + 5.48] = 0.6933$

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